Chemml Enqineenn~Sriencr Vol. 39. No 2. pp. 245-252. 1984
Printed in Great Britain
SAFE DESIGN OF COOLED TUBULAR REACTORS
EXOTHERMIC, MULTIPLE REACTIONS;
PARALLEL
REACTIONS-II
THE
DESIGN
AND OPERATION
OF AN ETHYLENE
K. R. WESTERTERP
Chemical Reaction
OXIDE
REACTOR
and K. J. PTAS&KI
Engineering Laboratories, Department of Chemical Engineering,
Technology, 7500 AE Enschede, The Netherlands
(Received 23 December
FOR
1982; accepted
Twenre University of
17 May 1983)
Abstract--ln
part I a model and criteria have been developed for the safe design and operation of cooled tubular
reactors for multiple reactions of the parallel type. In this Part II the model is extended to parallel reactions with an
arbitrary stoichiometry.
The results are applied to the industrial process of the ethylene oxidation with pure
oxygen. It is shown that the criteria derived in part I lead to useful guidelines for the design and operation of an
ethylene oxide reactor.
system of two parallel reactions:
DETERMINATION OF THE TUBE DIAMETER FOR AN
KlTNLENE OXIDE REACTOR
In Part I[l]
a model has been derived
for the
design and operation of multiple reactions of the parallel
type in a cooled tubular reactor. This model will now be
applied to the Ethylene Oxide reactor. In Part I two
selectivity
criteria were developed
for the pseudohomogeneous
model of the cooled tubular reactor in
which the reactions were assumed to have stoichiometric
coefficients equal to one. In order to apply the derived
criteria to the ethylene oxidation,
where the stoichiometric
coefficients differ from one, we have to
reformulate
these criteria for a more general
stoichiometry. This has been done in the appendix.
The industrial production of ethylene oxide is based on
the direct oxidation of ethylene in the gas phase with a
silver-based catalyst. In this oxidation process either air
or pure oxygen is used. It has been shown[2,3] that the
process using oxygen is more economical than the airbased process. Packed-bed,
multitubular cooled reactors
are used in the oxygen-based process and an excess of
ethylene is applied. Non-converted
ethylene is recycled.
The main by-products are Co2 and Hz0 formed according to:
CA0
CH/
-,
’
:
O2 + ~C~H~LP.~CZH&
o~++~H$-+;CO~+~H~O
- 210.3 MJ
- 473.0 MJ
(2)
(3)
which corresponds to the general parallel reaction system. The reaction
rate
expressions
reported
in
literature[4] range from purely empirical correlations to
complicated rate expressions of the Langmuir-Hinshelwood type. At a large excess of ethylene as applied in
the oxygen-based oxidation units, literature [S-7] agrees
that the rate equations simplify to first order kinetics in
the oxygen concentration,
so that in this case R,,+ =
kPCOl and R,, = kxCm. From the literature data we
selected the rate expressions
reported in Table 1, in
which also the system parameters and the chosen reactor
design data are given. We will now use the criteria
derived to determine safe tube diameters for a differential selectivity in the hot spot of SbB = 0.70. The reactor
inlet temperature is assumed to be equal to T,. For the
prescribed value of the differential selectivity Sb, = 0.70
the value of the differential reciprocal selectivity ratio
based on ethylene as the key-component
is:
(1)
CO1 + H20
Most kinetic studies[4] agree on the predominance of
the parallel reactions and the combustion of ethylene
oxide can be neglected under industrial reaction conditions, so we simplified the reaction scheme (1) to a
The kinetics of reactions (2) and (3) are controlled by the
oxygen concentration,
therefore it is convenient to use
oxygen as the key-component
and the maximum allowable differential
reciprocal
selectivity
ratio (Shr=lno.
K. R. WESTERTERP
Table
I. Values
-mp
of system
210
1.32*10-4
kl?
P
w 1.50
H’
= 2.25
c
=
P
and design
ro/k.ml
*
and
parameters
02
-AHx
m’/kg
s
TR
I.16
kJ/kg
= (E)
(S&)B
The maximum allowable
eqn (A9):
is calculated
~~(P-l)-ln
[
from
=
1
YAP - 1)
T mn =
the
-
473
nr/kool
-
546
K
kg/m’
Table 2. Reactor configurations designed according to
concentraiicmin
Oxygen
,“!&
*t
919
VelocLty
the
u.
feed
=
conversion
xu
= 0.40
md = 0.70.
Tpa
= 534 r.
02
reactor
vol.
,.4,
*
lo,J
kmols
as the design value for the reactor. For standard tube
diameters and for X AL = 0.40 sets of cooling medium
temperatures
and reactor lengths are given in Table 2.
The overall heat transfer coefficient has been calculated
as outlined in [8]. We assumed the reactor to produce
The minimum cooling temperature is calculated from eqn
(A12) resulting in (T,),i, = 0.8963 or (T,),i, = 489.4 K
SLlpxfiCidl
reactor
dtCaa
or T,, = 533.5 K (260.X).
Oxygen
oxide
L’(Trm- Tc) =
0.977
I,,
ethylene
(216.4”C) for Da,lDu,i, = 5. The parameters P1,z in the
criterion (AlO) are P1 = 1.00 and P2 = 0.973 for the
average values of T, = 503 K and AT,d = 0.80. As P, =
Pz and since ATod is high compared to (T,, -T,), we
will use for P the value P = 1.00. We now find with eqn
(AlO):
= & .0.429 = 2.571
temperature
for
= 850
Cd
K
PTASI~~SK~
= 13.2
TP
From eqn (A14) we get (S;rP),.:
(S&),,,o
K. J.
1.3
G,,
-
6.0
ml
per
the selectivity
criterion
cent
m/s
din&J3
I’0.40
s
es
1”
24.3
248
516
1.85
5.9
1%”
38.1
297
506
2.66
7.8
2”
49.3
290
497
3.72
11.2
0.766
2lr”
59.0
282
189
5.14
16.4
0.790
3”
72.7
269
475
6.91
31.5
0.829
0.717
0.719
0.740
1 ”
n
II
516
1.82
5.7
1%”
*
n
50-I
2.58
7.4
0.736
2 ”
.,
.I
499
3.50
10.1
0.758
25”
3 ‘.
II
.I
I
m
491
4.68
13.6
0.778
479
7.50
24.9
0.815
Safe design of cooled tubular reactors
steam, so the coolant is boiling water. Figure 1 presents
the relationships between the conversion X,, the reactor
temperature
T and the integral selectivity
S,, as a
function of the reactor length for the standard tube
diameters. We see from Table 2, that a 2.5” tube already
requires a cooling medium temperature of 489 K, which
is so low that excessively large tube lengths are required
for the conversion chosen. Moreover, we observe that
the integral selectivity increases with increasing tube
diameters; this is due to the lower average temperature
levels in the reactor for the larger diameters,
which
favours the desired reaction. Further the lower coolant
temperatures
move the hot spot temperature
further
away from T,,. For an integral selectivity of Sen -0.76
and a feed concentration
of 6 mole % of oxygen the
allowable nominal tube diameters range from l-5 to 2.5”.
247
We will select a reactor with 2” tubes of 12 m length for our
following considerations.
The capacity of the reactor, of
course, is determined by the total number of parallel tubes.
In Table 2 also the results obtained are given if the
second criterion is used. The difference in the results for
the two criteria is rather small; this in general is not the
case, but here ATad is so high that the correction term in
the second criterion with respect to the first criterion is
small.
OPERATION OF THE REACTOR
According to the aforementioned
design method based
on a selectivity criterion we will consider a reactor
design with 2” tubes of 12 m. length operating at a feed
concentration
of 6 ‘mole % of oxygen and a cooling
medium temperature of 473 K.
260
1
240-
T, ‘C
23c-
226
3”
ZOO!
0
2
4
6
6
10
12
2. m
(b)
d, = 3”
Fig. I. Oxygen conversion (a), temperature profiles (b) and integral selectivily (c) as a function of the reactor
length and the tube diameter for the ethylene oxide reactor (COO=6.0% mol, UII= 1.3 m/s, P = 1.0 MPa).
14
K. R.
248
WE~ERTERP
Runaway
We first check on runaway at design conditions by
increasing the oxygen concentration
in the feed and
keeping U ( T,,,, - T,)ld, constant. Results are given in
Fig. 2, which shows that runaway occurs at 7.9 mole %
& in the feed. Hence, at the proposed design conditions
the reactor operates completely safe. Moreover, the integral selectivity Spe is the highest at the oxygen concentration of 6 mol % as can be seen from Fig. 2(c).
Varying reactor loads
Another important operation problem are the reaction
conditions to be chosen at varying loads. We will con-
and K. J. PTASIASKI
sider two reactor load changes of 50 and 150% of the
design rate u0 = 1.30 m/s. We should be aware that a
variation in reactor load results in a change in the overall
heat transfer coefficient. According to selectivity criterion (AlO) a proper reactor operation requires keeping
the term U(T,,,,- T,)ld, CA0 constant and in our case
equal ‘to 1.47 * 10’ Jlkmo1.s in order to maintain the
required selectivity and safe operation. Therefore the
cooling medium temperature should be adjusted for the
change in the heat transfer coefficient as a result of the
change in the reactor load. In Table 3 cooling medium
temperatures
calculated
from
U(T,,,, - Tc)ld,Cao =
1.47 * 10’ Jlkmo1.s are given for the new reactor loads. In
T .902-
06
x,
.oQQ
I
280.
I
;
:494m
270.
T(OC)
2.m
(a)
230
Tc
i
6
i
t5
lb
2, m
(b)
1494m
0.60
I
0
2
4
1
6
8
lo
4
12
Fig. 2. Oxygen conversion (a), temperature profiles (b) and reactor selectivity (c) in the ethylene oxide reactorasa
function of the tube length; effect of oxygen inlet concentration Ud, = 2”. uo = 1.3m/s, P = 1.0MPa).
1
Safe design of cooled tubular reactors
Table
3. Selectivity and conversion in an ethylene oxide reactor
with 2” tubes of 12 m length, keeping U(T,, -T,)~JY,AJ, constant and at varying reactor loads.
T
”
“0
lil,S
x
c
s
RL
PB
K
Wl*.X
0.65
196
480
0.39
0.815
1.30
290
497
0.42
0.766
1.95
368
505
0.40
0.744
249
Fig. 3 is shown what the new conditions are-the
solid
lines-and
also what would happen-the
dotted lines-if
the coolant temperatures were not adjusted according to
the criterion and were kept constant at T, = 497 K. It can
be seen from the solid curves that operation of the
reactor adhering to criterion (AlO) leads to safe operation without runaway and with high selectivities. For the
lower load of u0 = 0.65 m/s the conversion is decreased
(Fig. 3a) due to lower average temperature tevel (Fig. 3b)
despite the longer residence time. On the other hand
at the higher load of LI,,= 1.95 m/s the conversion
is
0.6
260
0,5-
X*
I
04.
I 065
2
m/s
4
6
8
x)
2. m
*ljr----=-~
(a)
2co,1
!
4
1
2
0
I
6
1
8
I
lo
I ‘1,73 m
060
0
:,
2
4
I
I
I
6
8
10
’
Fig. 3. Oxygen conversion (a), temperature profiles (b) and reactor selectivity (c) as a function of the reactor length
and its load for the ethylene oxide reactor (solid lines calculated according to criteria, dotted lines-keeping
T,
constant); dr = 2”. CAO = 6% mol, P = I MPa).
K. R.
250
WESTERTERP
and K J.
PTASI~KI
entrance of the reactor and consequently
the length of
the tube-or
cooling area-available
to remove heat at
the highest heat production rates is also reduced. But
also the heat transfer coefficient is reduced at the lower
bow rate. The combination of these two effects in the
first part of the reactor results in conditions which are
not adequate anymore to keep the hot spot within acceptable limits and to prevent runaway.
Figure 3 demonstrates the strong influence of the gas
flow rates through the reactor. Temperature
profiles,
conversions and integral selectivities are all affected in a
decreased (Fig. 3a) due to shorter residence time and
despite the higher average temperature level (Fig. 3b). If
the coolant temperature
is not adjusted, decreasing the
toad to 50% leads to immediate runaway because of the
reduction of the overall heat transfer coefficient at lower
gas flow rates.
This may seem an unexpected result because reducing
the load also results in a reduction of the total heat
production in the reactor, so we would expect less severe
conditions and a more safe operation. This is not true. At
reducing the flow rate the hot spot moves towards the
07
0
4
2
0
6
8
10
12
2
4
2.m
(a)
0.80
se
I
I
0
2
I
4.
6
8
10
4
0
2. m
Fig. 4. Oxygen
conversion
(b)
(a), temperature profiles (b) and integral selectivity
pressure and its length (d, = 1.5”, CA0 = 6% mot, uo =
I
,
6
8
10
2.m
(c)
Cc) as a function
1.3m/s).
of the reactor
Safe design of cooled tubular reactors
Table 4. Selectivity and conversion
P
251
in an ethylene oxide reactor with 1.5” tubes of 12 m length, keeping U(T,,, T,)/dt CAMug = 1.3 m/s, T,. = 534 K.
“%A
=c
u
W/m%
iea
x
Lo.4o
K
A,12
s
pa,12
m
1.0
0.79
297
506
0.53
0.743
2.0
0.81
441
497
11.4
0.41
0.767
3.0
0.82
553
489
15.6
0.33
0.787
different way. It is a matter of overall plant economics
which combination of conversion and selectivity is best
or in other words which gas flow rate (number of tubes in
the reactor for a desired production)
represents
an
economic optimum.
The influence of the reactor pressure
In our previous calculations we used a reactor pressure of 1.0 MPa. It is known that in industrial practice
frequently higher reactor pressures are applied. In Fig. 4
and Table 4 therefore results are given for design pressures of 2.0 and 3.0 MPa and compared with the 1.0 MPa
case. In these figures a nominal tube diameter of 1.5 in. and
a length of 12m are taken and conditions are chosen
according to criterion (AIO). In this case 2 in. tubes would
give far too low conversions at the higher reactor pressures. We see that the reactor selectivity is improved at
higher pressures
at the expense of the conversion
obtained. We conclude from these figures that the reactor pressure is a very important variable, but a correct
choice can only be made on economic grounds taking
a.o. compression costs, reactor construction costs and
selectivities obtained into account.
7.E
S&
(S&p)B
v
differential reciprocal
selectivity
ratio (based on
A as a key-reactant)
differential reciprocal selectivity ratio (based on
B as a key-reactant)
stoichiometric coefficient
Subscripts
B reactant
[I] Westerterp
K. R. and Ptasinski, K.J., C%em. Engn,q Sci. 198439
235.
[2] Gans M. and Ozero B. J.. Hydrocurbon Proc. 1976 S(3) 73.
131 DeMaglie B., Hydrocarbon Proc. 1976 S(3) 78.
[4] Voge H. H. and Adams Ch. R., A&m
Cataf. 1967 17 151.
[S] Sattertield Ch. N., Hetero~enenus
Catnlysis in Pmrric~.
McGraw-Hill,
[61 Verma A. and
[7] Miller S. A.,
London 1969.
[81 Westerterp K.
New York 1980.
Kahaguine S., J.Cataf. 1973 30 430.
Ethylenu and its industrial Derivatiues.
R., van Swaaij W. P. M. and Beenackers A. A. C.
and Operation. Wiley. New York
M.. Chemical ReactorDesign
1983.
APPENDIX
We consider reactions
From the discussions presented we may conclude that
the criterion U(T,, ~ T,)/d, CA0 = constant leads to very
useful results for the design of reactors for multiple,
par&e1 reactions
and also for the operation
of existing
reactors in order to achieve optimum operating conditions. In all cases where according to the criterion the
coolant temperature has to be lowered the reactor selectivity is improved at the expense of the total conversion.
Moreover, we can observe from the results given that the
ratio of the integral to the differential selectivity is
strongly influenced by the ratio Da,/Da,;,
or T,,/T,.
The method outlined in part I is restricted to parallel
reactions for which the kinetics are of the first order or
can be fitted reasonably well by first order kinetics. For
consecutive
reactions we soon will publish a similar
treatment.
Benn,
of the following type:
Both reactions are irreversible, exothermic and of the first order
in reactant A. The heat balance for the pseudo-homogeneous
model of the cooled, tubular reactor is:
Here the heats of reactions AHp and AHx of both reactions are
now based on the conversion of one kmole of key-reactant A.
We introduce the conversions to the products P and X with
respect to reactant A, w,hich are defined by:
The
dimensionless
equations,
which
describe
the
reactor
behavinur are:
NOTATION
For the symbols
symbols,
introduced
we used we refer
in this part, are:
to Part
I[]].
(A4)
New
qg = 2 DalcP(l- xp -Xx)
S Pi3 selectivity based on B as a key-reactant (Pdesired product)
SbB differential selectivity based on B as a keyreactant (P-desired product)
g
= DaAT,d
(AS)
~nt~HnP)(l-Xp-X~)-D~U.(T-TI)
646)
K. R. WESERTEKP and K J PTASI~KI
252
After introducing the total conversion of the reactant A (Xn =
Xp + Xx) the relation between the reaction temperature and the
conversion XA can be found
in which
holds:
PI =
I for the first criterion and for the second one
Pz=l-
T ma
-Tc *
1+
$ Kc*-’
hT,d
(All)
, + ‘p H&-I’
KY
(A7)
The differential reciprocal selectivity ratio for the reactions
is found by dividing eqn (As) by (A4):
dXx
-_=S
dXp
can be found
by
j, =Jp“.
VP(P =
1)
in
to
as
If
which T, = [l -(In ~~)/y~]-’ and further a practical value has
be inserted for Dnc/Darnin. The differential selectivity ratio SkF
used in the criteria is based on reactant A as key component.
the second reactant B is the more valuable raw material, then
B should be chosen as key-reactant.
The differential reciprocal
selectivity ratio (S,&)n based on El is given by:
tA9)
v&h - 1)- In
and the selectivity
temperature
(Al)
The maximum allowable differential selectivity ratio (Sj,),,
is
related to the maximum allowable temperature T,., which is now
defined by:
T Ino
Similarly the minimum coolant
solving the implicit equation:
(Al3)
criteria by:
The relation between the two selectivities Sjcp and (Skp;,)a can
directly be obtained from eqns (A8) and (A13):
(Al’3
L414)